[name]Arthur[/name]: I really love [name]Arthur[/name], and think it’s a great option for you…
[name]Moses[/name]: If you’re going for balance, to me, [name]Moses[/name] is heavily weighted toward Judaism.
[name]William[/name]: [name]Love[/name]…
[name]Israel[/name]: See [name]Moses[/name]. I think either name could be paired with a one of your more non-denominational names.
[name]Charles[/name]: Great…
[name]Samuel[/name]: I love [name]Samuel[/name], too!
[name]Lev[/name]: To me, this one leans towards Judaism, too.
[name]Edward[/name]: I absolutely love [name]Edward[/name]!
It’s one of my all-time favorites. 
Girls
[name]Charlotte[/name]: I love this name, and think it strikes a perfect balance…
[name]Miriam[/name]: Due to its Old Testament roots, I do associate it with Judaism, but I think it’s less overtly associated with Judaism than [name]Moses[/name] or [name]Israel[/name].
[name]Blythe[/name]: I [name]LOVE[/name] [name]Blythe[/name]! 
[name]Aviva[/name]: I think it’s beautiful, but it doesn’t strike a balance to me.
[name]Scarlet[/name]: I love this option, too!
[name]Esther[/name]: See [name]Miriam[/name].
[name]Elizabeth[/name]: [name]Lovely[/name]…
[name]Chava[/name]: On your girls’ list, this one feels the least balanced to me, and I think that pronunciation issues may arise with the Ch part.
[name]Aurelia[/name]: I think this is beautiful.
From your list, I really love [name]Charlotte[/name] [name]Blythe[/name] and [name]Aurelia[/name] [name]Blythe[/name], as well as [name]Scarlett[/name] [name]Elizabeth[/name].
I’m Jewish, too, so to me, a name feels like a blend of being both Jewish and American (or British, in your case) as long as it’s not an overtly [name]Christian[/name] (Catholic, etc.) name, such as [name]Christine[/name], [name]Christina[/name], [name]Evangeline[/name], etc. I personally feel that because most classic/vintage names have been used throughout time by Jewish people (and people of all religions, of course), I can use them and still honor my roots.
[name]Amelia[/name]
[name]Anneliese[/name] ([name]Anne[/name] [name]Frank[/name]'s full first name)
[name]Annabelle[/name]
[name]Beatrice[/name]/[name]Beatrix[/name]
[name]Cora[/name]/[name]Cordelia[/name]
[name]Clara[/name]
[name]Dahlia[/name] (the [name]Dalia[/name] spelling is Hebrew)
[name]Daphne[/name]
[name]Eleanora[/name]
[name]Eve[/name]
[name]Evelyn[/name]
[name]Eliza[/name] (Hebrew)
[name]Frances[/name]
[name]Felicity[/name]
[name]Flora[/name]
[name]Genevieve[/name] (nn [name]Eve[/name] or [name]Evie[/name], which is Hebrew)
[name]Georgiana[/name]
[name]Gabriella[/name] (Nameberry lists iit as Italian, but I know it has Hebrew roots, too, like [name]Gabriel[/name])
[name]Helena[/name]
[name]Hope[/name]
[name]Ivy[/name]
[name]Iris[/name]
[name]Isadora[/name]
[name]Julia[/name]
[name]Josephine[/name] (I didn’t even realize this is Hebrew…)
[name]Louisa[/name]
[name]Lucy[/name]
[name]Laura[/name]
[name]Marielle[/name]
[name]Nora[/name]
[name]Phoebe[/name]
[name]Pearl[/name]
[name]Rose[/name]
[name]Rosalie[/name]
[name]Susannah[/name]
[name]Sally[/name]
[name]Stella[/name]
[name]Tess[/name]
[name]Violet[/name]
[name]Vivian[/name] (means “life,” like [name]Chaya[/name] and [name]Chava[/name])
[name]Andrew[/name]
[name]Conrad[/name]
[name]Dexter[/name]
[name]Everett[/name]
[name]Elias[/name] (nn [name]Eli[/name])
[name]Franklin[/name]
[name]Henry[/name]
[name]Leo[/name]
[name]Milo[/name]
[name]Miles[/name]
[name]Maxwell[/name]
[name]Oliver[/name]
[name]Phineas[/name]
[name]Simon[/name]
[name]Theodore[/name]
Some names I associate with a bit more Judaism (I apologize for repeats), but that still feel balanced:
[name]Abigail[/name] (popular, though)
[name]Eden[/name] (not my personal style, but I think it’s pretty)
[name]Eliana[/name]
[name]Raphaela[/name]
[name]Seraphina[/name]
Some more that I love but that feel less balanced in terms of Jewish/British:
[name]Shoshana[/name]
[name]Talia[/name]
Some more boys’ names that feel more Jewish than the others, but still balanced:
[name]Abraham[/name]
[name]Benjamin[/name]
[name]David[/name]
[name]Eli[/name]
[name]Gabriel[/name]
[name]Gideon[/name]
[name]Nathaniel[/name]
[name]Noah[/name] (popular, though)
[name]Samson[/name]
[name]Solomon[/name]
[name]Tobias[/name]
Good luck! 